Two mod-p Johnson filtrations

2014/02/18 by Cooper, James · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1402.4186

Abstract

We consider two mod-p central series of the free group given by Stallings and Zassenhaus. Applying these series to definitions of Dennis Johnson's filtration of the mapping class group we obtain two mod-p Johnson filtrations. Further, we adapt the definition of the Johnson homomorphisms to obtain mod-p Johnson homomorphisms. We calculate the image of the first of these homomorphisms. We give generators for the kernels of these homomorphisms as well. We restrict the range of our mod-p Johnson homomorphisms using work of Morita. We finally prove the announced result of Perron that a rational homology 3-sphere may be given as a Heegaard splitting with gluing map coming from certain members of our mod-p Johnson filtrations.

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• Odd-primary torsion in the homology of unordered configurations on the torus

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• Double Johnson filtrations for mapping class groups
• Torelli group, Johnson kernel and invariants of homology spheres
• Finite type invariants in low degrees and the Johnson filtration
• p-Johnson homomorphisms and pro-p groups
• A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics